Other ways besides key logger
My own bank offers an "enhanced security" mode which handles the session in a new window that is removed from memory after signout -- and they recommend it specifically for cybercafes. Otherwise the next user can retrieve all sorts of interesting banking details via the back button.
I don't know about Dubai, but if a key logger was installed in a cybercafe machine and used to record banking details in North America or Europe, the police and bank fraud investigators would have said cybercafe turned inside out in no time.
Dubai does bill itself an an international banking center; so there might be a possibility the authorities would take action.
Besides a key logger, it is also possible that your userid and password were caught by a video camera or shoulder surfing.